Abstract

The dynamic evolution of bright spatial solitons induced by the transverse shifting of the beam is investigated. Transverse shifting can result in the formation and dynamic evolution of bright spatial solitons in photorefractive materials. To explain the phenomena, a uniform theoretical physical model is proposed. Numerical analysis results show that the beam shifting has strong influence on the formation and dynamic evolution of bright spatial solitons.

© 2013 Optical Society of America

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References

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  1. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
    [CrossRef]
  2. S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
    [CrossRef]
  3. K. Q. Lu, T. T. Tang, and Y. P. Zhang, “One-dimensional steady-state spatial solitons in photorefractive materials with an external applied field,” Phys. Rev. A 61, 053822 (2000).
    [CrossRef]
  4. J.-S. Liu and Z.-H. Hao, “Effect of temperature on the evolution of bright and dark screening-photovoltaic spatial solitons,” Chin. Phys. 11, 254–259 (2002).
    [CrossRef]
  5. M. Facao and D. F. Paker, “Stability of screening solitons in photorefractive media,” Phys. Rev. E 68, 016610 (2003).
    [CrossRef]
  6. F.-W. Sheu and M.-F. Shih, “Swinging optical spatial solitons in a biased photorefractive crystal,” J. Opt. A 9, 271–277 (2007).
    [CrossRef]
  7. E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
    [CrossRef]
  8. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2010).
    [CrossRef]
  9. R. A. Vazquez, R. R. Neurgaonkar, and M. D. Ewbank, “Photorefractive properties of SBN:60 systematically doped with rhodium,” J. Opt. Soc. Am. B 9, 1416–1427 (1992).
    [CrossRef]
  10. Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
    [CrossRef]
  11. Ch. Y. Gao, J. Q. Xu, J. Qiu, S. W. Liu, and G. F. Feng, “Shifting bright spatial solitons in LiNbO3,” Opt. Lett. 37, 3702–3704 (2012).
    [CrossRef]
  12. S. M. Kostritskii and O. G. Sevostyanov, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 517–522 (1997).
    [CrossRef]
  13. D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
    [CrossRef]
  14. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).
  15. L. Jinsong and L. Keqing, “Screening-photovoltaic spatial solitons in biased photovoltaic-photorefractive crystals and their self-deflection,” J. Opt. Soc. Am. B 16, 550–555 (1999).
    [CrossRef]
  16. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989), pp. 41–50.

2012

Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
[CrossRef]

Ch. Y. Gao, J. Q. Xu, J. Qiu, S. W. Liu, and G. F. Feng, “Shifting bright spatial solitons in LiNbO3,” Opt. Lett. 37, 3702–3704 (2012).
[CrossRef]

2010

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2010).
[CrossRef]

2007

F.-W. Sheu and M.-F. Shih, “Swinging optical spatial solitons in a biased photorefractive crystal,” J. Opt. A 9, 271–277 (2007).
[CrossRef]

2003

M. Facao and D. F. Paker, “Stability of screening solitons in photorefractive media,” Phys. Rev. E 68, 016610 (2003).
[CrossRef]

2002

J.-S. Liu and Z.-H. Hao, “Effect of temperature on the evolution of bright and dark screening-photovoltaic spatial solitons,” Chin. Phys. 11, 254–259 (2002).
[CrossRef]

2000

K. Q. Lu, T. T. Tang, and Y. P. Zhang, “One-dimensional steady-state spatial solitons in photorefractive materials with an external applied field,” Phys. Rev. A 61, 053822 (2000).
[CrossRef]

1999

1997

S. M. Kostritskii and O. G. Sevostyanov, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 517–522 (1997).
[CrossRef]

1995

D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
[CrossRef]

S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
[CrossRef]

1994

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef]

1992

Agranat, A. J.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2010).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989), pp. 41–50.

Alonzo, M.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

Argiolas, N.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

Bazzan, M.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

Carvalho, M. I.

Chauvet, M.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

Christodoulides, D. N.

S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
[CrossRef]

Conti, C.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2010).
[CrossRef]

Crosignani, B.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef]

DelRe, E.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2010).
[CrossRef]

Devaux, F.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

DiPorto, P.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef]

Ewbank, M. D.

Facao, M.

M. Facao and D. F. Paker, “Stability of screening solitons in photorefractive media,” Phys. Rev. E 68, 016610 (2003).
[CrossRef]

Fazio, E.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

Feng, G. F.

Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
[CrossRef]

Ch. Y. Gao, J. Q. Xu, J. Qiu, S. W. Liu, and G. F. Feng, “Shifting bright spatial solitons in LiNbO3,” Opt. Lett. 37, 3702–3704 (2012).
[CrossRef]

Gao, Ch. Y.

Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
[CrossRef]

Ch. Y. Gao, J. Q. Xu, J. Qiu, S. W. Liu, and G. F. Feng, “Shifting bright spatial solitons in LiNbO3,” Opt. Lett. 37, 3702–3704 (2012).
[CrossRef]

Hao, Z.-H.

J.-S. Liu and Z.-H. Hao, “Effect of temperature on the evolution of bright and dark screening-photovoltaic spatial solitons,” Chin. Phys. 11, 254–259 (2002).
[CrossRef]

Jinsong, L.

Keqing, L.

Kostritskii, S. M.

S. M. Kostritskii and O. G. Sevostyanov, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 517–522 (1997).
[CrossRef]

Liu, J.-S.

J.-S. Liu and Z.-H. Hao, “Effect of temperature on the evolution of bright and dark screening-photovoltaic spatial solitons,” Chin. Phys. 11, 254–259 (2002).
[CrossRef]

Liu, S. W.

Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
[CrossRef]

Ch. Y. Gao, J. Q. Xu, J. Qiu, S. W. Liu, and G. F. Feng, “Shifting bright spatial solitons in LiNbO3,” Opt. Lett. 37, 3702–3704 (2012).
[CrossRef]

Lu, K. Q.

K. Q. Lu, T. T. Tang, and Y. P. Zhang, “One-dimensional steady-state spatial solitons in photorefractive materials with an external applied field,” Phys. Rev. A 61, 053822 (2000).
[CrossRef]

Neurgaonkar, R. R.

Paker, D. F.

M. Facao and D. F. Paker, “Stability of screening solitons in photorefractive media,” Phys. Rev. E 68, 016610 (2003).
[CrossRef]

Qiu, J.

Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
[CrossRef]

Ch. Y. Gao, J. Q. Xu, J. Qiu, S. W. Liu, and G. F. Feng, “Shifting bright spatial solitons in LiNbO3,” Opt. Lett. 37, 3702–3704 (2012).
[CrossRef]

Sada, C.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

Segev, M.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef]

Sevostyanov, O. G.

S. M. Kostritskii and O. G. Sevostyanov, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 517–522 (1997).
[CrossRef]

Sheu, F.-W.

F.-W. Sheu and M.-F. Shih, “Swinging optical spatial solitons in a biased photorefractive crystal,” J. Opt. A 9, 271–277 (2007).
[CrossRef]

Shih, M.-F.

F.-W. Sheu and M.-F. Shih, “Swinging optical spatial solitons in a biased photorefractive crystal,” J. Opt. A 9, 271–277 (2007).
[CrossRef]

Singh, S. R.

S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
[CrossRef]

Spinozzi, E.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2010).
[CrossRef]

Tang, T. T.

K. Q. Lu, T. T. Tang, and Y. P. Zhang, “One-dimensional steady-state spatial solitons in photorefractive materials with an external applied field,” Phys. Rev. A 61, 053822 (2000).
[CrossRef]

Toncelli, A.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

Valley, G. C.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef]

Vazquez, R. A.

Wang, A. K.

Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
[CrossRef]

Xu, J. Q.

Ch. Y. Gao, J. Q. Xu, J. Qiu, S. W. Liu, and G. F. Feng, “Shifting bright spatial solitons in LiNbO3,” Opt. Lett. 37, 3702–3704 (2012).
[CrossRef]

Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
[CrossRef]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef]

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

Zhang, Y. P.

K. Q. Lu, T. T. Tang, and Y. P. Zhang, “One-dimensional steady-state spatial solitons in photorefractive materials with an external applied field,” Phys. Rev. A 61, 053822 (2000).
[CrossRef]

Appl. Phys. B

Ch. Y. Gao, J. Q. Xu, G. F. Feng, J. Qiu, S. W. Liu, and A. K. Wang, “Dynamic behavior of spatial bright solitons in a biased transversely shifting photorefractive crystal,” Appl. Phys. B 107, 779–784 (2012).
[CrossRef]

S. M. Kostritskii and O. G. Sevostyanov, “Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals,” Appl. Phys. B 65, 517–522 (1997).
[CrossRef]

Appl. Phys. Lett.

E. Fazio, M. Alonzo, F. Devaux, A. Toncelli, N. Argiolas, M. Bazzan, C. Sada, and M. Chauvet, “Luminescence-induced photorefractive spatial solitons,” Appl. Phys. Lett. 96, 091107 (2010).
[CrossRef]

Chin. Phys.

J.-S. Liu and Z.-H. Hao, “Effect of temperature on the evolution of bright and dark screening-photovoltaic spatial solitons,” Chin. Phys. 11, 254–259 (2002).
[CrossRef]

J. Opt. A

F.-W. Sheu and M.-F. Shih, “Swinging optical spatial solitons in a biased photorefractive crystal,” J. Opt. A 9, 271–277 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2010).
[CrossRef]

Opt. Commun.

S. R. Singh and D. N. Christodoulides, “Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,” Opt. Commun. 118, 569–576 (1995).
[CrossRef]

Opt. Lett.

Phys. Rev. A

K. Q. Lu, T. T. Tang, and Y. P. Zhang, “One-dimensional steady-state spatial solitons in photorefractive materials with an external applied field,” Phys. Rev. A 61, 053822 (2000).
[CrossRef]

Phys. Rev. E

M. Facao and D. F. Paker, “Stability of screening solitons in photorefractive media,” Phys. Rev. E 68, 016610 (2003).
[CrossRef]

Phys. Rev. Lett.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef]

Other

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989), pp. 41–50.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Shifting time t and κ(v), where we assume that xd=0.005mm, v=0.28mm/s, and τ=0.03s in our experimental condition. (b) Output spot 10 cm away from the crystal (the focal length of the lens used in the experiment is 20 mm) with the shifting velocity 0.28mm/s at (i) 0 s, (ii) 133 ms, (iii) 212 ms, (iv) 418 ms, (v) 536 ms, (vi) 664 ms in Fe:LiNbO3.

Fig. 2.
Fig. 2.

Shifting velocity v and κ(v) in steady states, where xd=0.005mm and τ=0.03s.

Fig. 3.
Fig. 3.

Normalized intensity profiles of bright spatial solitons for r=0.1 and v=0.3mm/s, 0.4mm/s, 0.5mm/s, and 0.6mm/s as a function of s=x/x0, E0=40kV/m, and x0=10μm.

Fig. 4.
Fig. 4.

Dynamical evolution of a bright spatial soliton at (a) v=0.30mm/s, (b) v=0.29mm/s, (c) v=0.31mm/s, (d) v=0.2mm/s, (e) v=0.4mm/s, (f) v=0.5mm/s. The input bright spatial solitary state is obtained originally from Eq. (17) with α=0, r=0.1, and β=2.98.

Fig. 5.
Fig. 5.

Intensity profiles of bright spatial solitons formed in the crystal with the input state α=0, r=0.1, and β=2.98 at ξ=20.

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

Esc0(t)=Esc0exp(tτ)=Esc0exp(xvτ),
Eex=Esc0exp[(m1)xdvτ]++Esc0exp(2xdvτ)+Esc0exp(xdvτ)=exp(xdvτ)exp(mxdvτ)1exp(xdvτ)Esc0=κ(v)Esc0,
κ(v)=exp(xdvτ)exp(mxdvτ)1exp(xdvτ)(t=mxdv).
ND+t=(sI+β)(NDND+)γRND+n^,
J=qμn^E+kBTμn^+Jph+Jex,
·(εE)=q(ND+NAn^),
n=s(I+Id)(NDND+)γRND+,
n^0=s(I+Id)(NDNA)γRNA,
J=qμn^(E+kBTqn^dn^dx+EpII+Id+Eex)=J=qμn^0(E0+EpII+Id)(·J=0).
Esc=I+IdI+IdE0Eex+III+IdEpkBTqddxln(I+Id),=Esc0Eex,(Esc0=I+IdI+IdE0+III+IdEpkBTqddxln(I+Id)),
Esc=[1κ(v)][I+IdI+IdE0+III+IdEpkBTqddxln(I+Id)].
κ(v)=1exp(xdvτ)1.
2ikAz+2Ax2+k022neΔneA=0,
iUξ+122Us2β(ρ+1)11+|U|2Uαρ|U|21+|U|2U+γ11+|U|2|U|2sU=0,
β=12k02x02ne4γ33E0[1κ(v)],
α=12k02x02ne4γ33Ep[1κ(v)],
γ=12k02x0ne4γ33[1κ(v)]kBTq.
iUξ+122Us2β(ρ+1)11+|U|2Uαρ|U|21+|U|2U=0.
[2(β+α)]1/2s=±y(s)1r1/2dy^[ln(1+ry^2)y^2ln(1+r)]1/2,
Esc=[1κ(v)]Esc0=[1κ(v)]IdI+IdE0,
iUξ+122Us28.625[1κ(v)]11+|U|2U=0.

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